Various studies have been conducted for simulating biomechanical phenomena, bioelectric phenomena, and others using numerical simulation analysis. For example, what is important for a heart to beat normally is that blood containing sufficient oxygen and substances that turn into energy is supplied to myocardium. Numerical simulation analysis enables predicting hemodynamics as to how much of blood ejected from the left ventricle each coronary artery surrounding a heart supplies to the myocardium. Such predictions support diagnosis to confirm whether sufficient blood is supplied to the myocardium of a patient suffering from stenosis of a blood vessel. At present, a blood flow in a blood vessel is measured by inserting a catheter into a body. Therefore, an alternative based on non-invasive simulation is expected.
A coronary artery model, which is one of inputs for a patient-specific coronary artery simulation, is represented by triangular faces (hereinafter, referred to as meshes), which form the shapes of aorta and coronary arteries, and tetrahedral volume elements. Elements of each part are given a different material number. A computer that creates a coronary artery model first extracts a cardiovascular area from a medical image. The computer then creates the shape of a heart and boundary surfaces with meshes, which are triangular faces, by reference to the extracted cardiovascular area, and generates volume elements on the basis of these.
Each individual has a different cardiovascular shape. Therefore, for example, a computer that creates a coronary artery model extracts the cardiovascular shape of a patient from medical images captured with a computed tomography (CT), magnetic resonance imaging (MRI), or another. Then, the computer creates a coronary artery model using triangular meshes by reference to the extracted area. In this connection, if meshes are large for a shape to be modeled, the coronary artery model may have a rough shape even though it actually has a smooth shape. In addition, two parts that are actually disconnected from each other may happen to connect to each other in the coronary artery model. To deal with these, the following technique is often employed: Sufficiently small meshes are first used to create a coronary artery model, and then the number of meshes is reduced according to the shape of the coronary artery model.
For example, a method for reducing the number of meshes is to sequentially select, on the basis of data on an isosurface of created triangles, the triangular meshes in ascending order of size, and then according to a preset reduction rate, remove the selected triangular mesh while confirming using the original three-dimensional data if the removal of the selected triangular mesh does not cause a big problem. In addition, there is another method that is to make two adjacent nodes overlap each other to merge them into one node. This method is called edge collapse (or edge contraction) since the new node is generated by collapsing one edge and combining its both end nodes.
See, for example, the following documents:
Japanese Laid-open Patent Publication No. 2003-323637; and
M. Garland and P. S. Heckbert, “Surface Simplification Using Quadric Error Metrics,” SIGGRAPH '97 Proceedings of the 24th annual conference on Computer graphics and interactive techniques, ACM Press, New York, 3-8 Aug. 1997, pp. 209-216.
In reducing the number of meshes with the edge collapse, a method of determining coordinates for a new node to be generated by collapsing an edge takes an important role. For example, consider the case where the coordinates of a middle point between two nodes connected by an edge is set as new coordinates. In this case, as the mesh reduction progresses, the coordinates of a point that more deviate from the original shape are set as the new coordinates, which results in losing the original shape. The above document, “Surface Simplification Using Quadric Error Metrics” by M. Garland and P. S. Heckbert, employs a technique of minimizing, with respect to each node, the sum of squares of distances (quadric error metric (QEM)) between the node and its adjacent planes including the node, in order to keep the original shape as much as possible. However, this technique collapses edges in ascending order of change in QEM to be caused by collapse, and therefore long narrow meshes are likely to be generated for a long thin shape like a coronary artery. Thus, large meshes (that are long on one side) are generated at an early stage. If the mesh reduction is further performed on such long narrow meshes, the shape becomes greatly different from the original shape. This problem occurs not only in the case of reducing the number of meshes in a coronary artery model to be used in a heart simulation but also in the case of reducing the number of meshes in a three-dimensional mesh model.